A contract isn't the signed piece of paper, it's a "meeting of minds", two legal entities (e.g. a corporation and a human) reach a common understanding in which things of value are exchanged. Working for money for example. In some places there may be a law explicitly requiring that for employment you're entitled to a piece of paper setting out the terms, but it remains the case that contracts of employment come into existence as a result of this meeting of minds not the piece of paper.
For example once when I was young I was hired by the following process. I see on the TV news that a chip fab I've worked in caught fire, damaging nearby buildings. There are a lot of fire engines but the blaze is under control. Then I get a phone call from a friend, "Mountbatten is on fire". "I saw that". "We're getting Zepler back tomorrow, once structural engineers sign off on it - can you be there 0900 sharp to salvage stuff and get the network back up?". "Can do. See you tomorrow".
No interview. No pieces of paper. No salary negotiation. But that's an employment contract, just some of the details not determined until later. I actually genuinely don't remember how long I worked that gig, it was a lot of fun although pretty different from what I do these days.
In court, forging evidence by relating a signature page to the wrong document so they can then lie to a court about it is not OK - their lawyers aren't going to want to have anything to do with that idea. Contrariwise, if you have an email back-and-forth, or even just a friend who remembers you talking about the change, you're in a good place because your story makes sense and the employer's story does not.
But mostly you aren't going to be in court. If you're confident the employer would try to actually fuck you over, and you're in the sort of work where you get to strike contract terms, walk away from that job. Nobody needs that.